Unit And Measurement
Measurement of physical quantities:
Physics
is a quantitative science, based on measurement of physical
quantities.Certain physical quantities have been chosen as fundamental
or base quantities. The fundamental quantities that are chosen are
Length, Mass, Time, electric current, thermodynamic temperature, amount
of substance, and luminous intensity.
Base quantity and Fundamental Units :
Each
base quantity is defined in terms of a certain basic arbitrarily
chosenbut properly standardised reference standard called unit (such as
metre,kilogram,second,ampere,
1. Length metre (m)
2. Mass kilogram (kg)
3. Time second (s)
4. Temperature kelvin (K)
5. Luminous candela (cd)
Intensity
6. Electric ampere (A)
Current
7. Amount of mole (mol)
Substance
Derived units :
Other
physical quantities derived from the base quantities can be expressed
as a combination of the base units and are called derived units.A
complete set of units both fundamental and derived units are called a
system of units. Example :- volume, density etc
International System of units :
*The
International System of units based on seven base unitsis at present
internationally acceptedunit system and is widely used throughout the
world. In computing any physical quantity the units for derived
quantities involved in the relationships are treated as though they were
algebraic quantities till the desired units are obtained
CGS System In this system, the unit of length is centimetre, the unit of mass is gram and the unit of time is second.
FPS System In this system, the unit of length is foot, the unit of mass is pound and the unit of time is second.
MKS System In this system, the unit of length is metre, the unit of mass is kilogram and the unit of time is second.
SI
System This system contain seven fundamental units and two
supplementary fundamental units. The SI units are used in all physical
measurements, for both the base quantitiesand the derived quantities
obtained from them. Certain derived units are expressed by means of SI
units of special names such as joule, newton, watt etc.
*
In computing any physical quantity the units for derived quantities
involved in the relationships are treated as though they were algebraic
quantities till the desired units are obtained
* In SI system that is System Internationale d’ Units there are 7 base units’ andtwo supplementary units.
SL/NO - Supplementary - Supplementary - Symb
Fundamental Unit
Quantities
1. - Plane Angle - radian - rad
2. - Solid Angle। - steradian। - sr
*
Direct and indirect methods can be used for the measurement of physical
quantities. In measured quantities while expressing theresult, the
accuracy and precision of measuring instrumentsalong with errors in
measurement should be taken into account.
* In measured and computed quantitiesproper significant figures only should be retained.
Use of Dimensional analysis:
*
The dimensions of base quantities and combination of these dimensions
describe the nature of physical quantities .Dimensional analysis can be
used to check the dimensional consistency of equations, deducing
relations among physical quantities etc. A dimensionally consistent
equation need not be actually an exact equation, but a dimensionally
wrong or inconsistent equation must be wrong.
Error:
The uncertainty in the measurement of a physical quantity is called an error.
The errors in measurement can be classified as (i) Systematic errors and (ii) Random errors
These are the errors that tend to be either positive or negative.Sources of systematic errors are
(i) Instrumental errors
(ii) Imperfection in experimental technique or procedure
(iii) Personal errors
RANDOM ERRORS :
Those errors which occur irregularly .These errors arise due to unpredictable fluctuations in experimental conditions
Least count error:
Least count error is the error associated with the resolution of the instrument.
Absolute error:
The
magnitude of the difference between the individual measurement and the
true value of the quantity is called the absolute error of the
measurement.
**Attachment
Mean Absolute Error:
The
arithmetic mean of all the absolute errors is taken as the final or
mean absolute error of the value of the physical quantity a. It is
represented by Δa mean
**Attachment
Relative error - it is the ratio of the mean absolute error to the true value.
Relative error = Δa mean/ a mean
Percentage Error : When the relative error is expressed in per cent, it is called the percentage error (δa).
Percentage error =( Δa mean/ a mean) ×100
COMBINATION OF ERRORS
ERROR OF A SUM OR A DIFFERENCE
When
two quantities are added or subtracted, the absolute error in the final
result is thesums of the absolute errors in the individual quantities.
IF Z=A+ B then the max possible error in Z, ∆Z =∆A + ∆B
IF Z=A- B then the max possible error in Z, ∆Z =∆A + ∆B
ERROR OF A PRODUCT OR A QUOTIENT -
When two quantities are multiplied or divided the relative error is the sum of the relative errors in the multipliers
Suppose Z= A*B or Z=A/B then the max relative error in ‘Z’ = ∆Z/Z= (∆A/A) + (∆B/B)
ERROR IN CASE OF A QUANTITY RAISED TO A POWER -
The relative error in a physical quantity raised to the power k is the k times the relative
error in the individual quantity.
Suppose Z = Ak
then ∆Z/Z = K (∆A/A)